Geodetic Surveying Made Plain

December 21, 2000
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A decade or two ago, I was the instructor for some introductory surveying courses at a community college. In the first class we would define “plane surveying” as surveying that did not take into consideration the curvature of earth, and “geodetic surveying” as that which did. That was about the only time the two categories received anywhere near equal attention. Oh, we would point out (still in that first lecture) some of the real-world evidence of a non-flat earth, such as the fact that the length of an 11.5-mile arc on the earth's surface is only five hundredths of a foot longer than its subtended chord, or that the sum of the angles in a spherical triangle on the earth’s surface having an area of 75 square miles is only one second greater than the angle sum of the same size plane triangle. (Even today I get a kick out of those dramatic tidbits. I’m sure a real geodesist would roll his or her eyes at such trivia!) But those examples were used as reasons for not focusing—no, for not mentioning—geodetic concepts for the rest of the semester. We would end the ten-minute token nod to geodetic surveying with the tongue-in-cheek remark, “Therefore, for this class, we will respect the time-honored principle handed down through the ages—that the earth is flat.” And, truth be known, that’s probably not a bad narrowing of a dauntingly broad subject.

But more than narrowing, it was simply that few rank-and-file surveyors in private practice ever had occasion to use geodetic concepts in their daily work. Even when we dutifully enrolled in the occasional State Plane Coordinate seminar, the principles quickly faded from memory from lack of use. If a surveyor from the general population had ever even heard of the geoid and its relationship to the ellipsoid, and where mean sea level fit into the picture, hearing about it was as far it went. We stayed proficient in the subjects we used everyday. But that … was then.

And this is now … boy, is it ever! That picture has changed and continues to change even as we discuss it. A trio of factors has pushed learning about geodetic surveying and its principles right up to the top of Mr. Everyday Surveyor’s to-do list. Perhaps the earliest of these three factors to emerge was the increasing requirement imposed at various jurisdictional levels that subdivisions, or in some cases all surveys of record, be tied to a master coordinate system. That system is generally State Plane or some other large, comprehensive coordinate system. Whatever the format, some knowledge of grid coordinates vs. surface coordinates, geodetic north vs. grid north, and the like, is essential for the surveyor to operate successfully in that sphere (no pun intended). Incidentally, I saw a question on rpls.com recently about this topic. The consensus of the dialog agreed that all surveys going onto a uniform system is coming in the not too distant future.

The primary reason for this uniform coordinate system requirement brings us to the second factor spotlighting geodetic surveying: the proliferation of Geographic Information Systems across the country. Some of us have seen first-hand how chaotic a GIS can be when the coordinate system is not fully understood. Or, if not chaotic, at least falling short of its intended use due to unreliable accuracies. Those problems are easily fixed with a stiff dose of geodetic surveying expertise.

The third and most important factor driving the emphasis on geodetic principles is of course the Global Positioning System. It’s fairly common knowledge that GPS is based on a worldwide coordinate system usually expressed in geographic coordinates (lats and longs), is incredibly accurate in geodetic applications, and uses a bunch of high-powered math to derive positions on the earth. All those points bear witness to the close relationship between GPS and geodetic surveying. “But,” I hear you say, “my GPS salesman says we can use his RTK system just like a conventional total station (given proper conditions) and that we don’t have to worry about all this geodetic business.” I agree with the first part of this statement, and the second as well, but with an asterisk—make that two asterisks—one for each part of the statement. Let’s break the issue down:

As to using RTK surveying just as one would use a conventional total station, yes you can if, and only if, you have a thorough grasp of the details of the analogy. By that I mean, for example, that you must understand that a single base receiver working with a single rover is creating a single baseline for each shot. What do we call that? Correct—a radial survey; we do them all the time with conventional equipment. But we do not make boundary surveys, for instance, with a single-shot radial survey. If a surveyor in my state of Texas set up a total station in the middle of a tract, made a single shot on each property corner and called it a boundary survey, that surveyor would be in violation of the rules set by the Texas Board of Professional Land Surveyors.

If we were able to see all the corners with conventional gear like we sometimes can with GPS’s no-line-of-sight benefit, we would do some industrial-strength verification of those shots, like shoot all the points again, maybe from a different setup point. Point being that while stand-alone radial surveys are acceptable for, say, a topo, they simply are not acceptable for boundaries or control. And you’d better understand when your work is at risk of falling under the “radial” heading. It all comes under the heading: “Use techniques, procedures and equipment appropriate to the surveying objectives.”

Okay, what about the “not worrying about this geodetic business” part? Right, you probably don’t have to worry about it as long as everything goes according to the plan. But let me ask a question: “Have you ever embarked upon a surveying project with a plan and had to modify the plan?” Okay, stop laughing—who hasn’t? As General Dwight D. Eisenhower once observed, “Battle plans are fine until the battle starts.” All this is not to imply that every time something goes wrong you need to start delving into the arcane nuts and bolts of GPS theory and become Mr. or Ms. Geodetic Surveyor. But it does make sense that you are better prepared to deal with glitches if you understand more than just what buttons to push.

Look … regardless of surveying implementation, at its heart GPS is measuring distances to satellites and fitting the trilaterated results into an earth-centered Cartesian coordinate system using a reference ellipsoid. I realize that some surveyors using GPS do so in the same plane surveying projects as they always have; their coordinate systems oriented to a local project only, with no pressing need to connect to the rest of the world. But I would hope that no surveyor would use a measurement system without having at least a good general understanding of how it works. And there’s plenty of evidence that such understanding is being sought by record numbers of the nation’s surveyors. Witness the throngs of attendees at seminars on GPS and related topics, and especially at sessions on State Plane Coordinates like the one conducted all over the country by Dave Doyle, senior geodesist with National Geodetic Survey. Those sessions are invariably packed.

Geodetic Surveying: Some Historical Perspective

Earlier I mentioned my fascination with round-earth trivia. Equally high on the fascination index is the wealth of lore and legend surrounding the old USC&GS (now NGS) and its efforts to establish reliable geodetic control nationwide. Most, if not all, geodetic surveyors agree that NAD83 and its upgrade, High Accuracy Reference Network are superior to (and should be used instead of) NAD27. But agreement is also widespread that the establishment of NAD27 was a remarkable achievement for its time. Imagine establishing first-order control almost exclusively with triangulation! How accurate must those angles have been turned! Listening to an account of mere routine field procedures can generate an out and out … well, thrill in the bones of almost any surveyor. Picture it: nighttime atop a Bilby tower or a mountain, occupying a point with a 40-pound Wild T3, huge by our standards but considered small when introduced, turning to as many as dozens of lights measuring angles read to a decimal part of a second on an optical micrometer, taking readings on each point with 16 different plate orientations … to us it’s the stuff of legends, but to those guys just another day’s—I mean night’s—work.

NGS’s parent agency, the National Oceanic and Atmospheric Administration maintains a fine historical website, with a large segment dedicated to USC&GS. It’s at www.history.noaa.gov and it’s highly recommended reading for anyone interested in such accounts.

A personal note: It is an honor for me to become a member of the POB editorial team. I look forward to a long and productive relationship with the most important members of POB’s circle: you, our readers.

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